Critical Points and Intervals of Increase

I. For $f(x)= x^3 - 3*x^2 + 4$, the derivative is $f'(x)= 3*x^2 - 6*x$ which yields critical points at $x=0$ and $x=2$.

II. The function f(x) is increasing on the intervals $(-\infty, 0)$ and $(2, \infty)$.

III. f(x) is decreasing on the interval $(0,2)$.

Which of the above statements is/are correct?